# Tài chính doanh nghiệp - Chapter 14: Bond prices and yields

Face or par value Coupon rate Zero coupon bond Compounding and payments Accrued Interest Indenture

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Chapter 14Bond Prices and YieldsFace or par valueCoupon rateZero coupon bondCompounding and paymentsAccrued InterestIndentureBond CharacteristicsDifferent Issuers of BondsU.S. TreasuryNotes and BondsCorporationsMunicipalitiesInternational Governments and CorporationsInnovative BondsIndexed BondsFloaters and Inverse FloatersSecured or unsecuredCall provisionConvertible provisionPut provision (putable bonds)Floating rate bondsSinking fundsProvisions of BondsPB = Price of the bondCt = interest or coupon paymentsT = number of periods to maturityy = semi-annual discount rate or the semi-annual yield to maturityBond PricingCt = 40 (SA)P = 1000T = 20 periodsr = 3% (SA) Price: 10-yr, 8% Coupon, Face = \$1,000Prices and Yields (required rates of return) have an inverse relationshipWhen yields get very high the value of the bond will be very low.When yields approach zero, the value of the bond approaches the sum of the cash flows.Bond Prices and YieldsPriceYieldPrices and Coupon RatesYield to MaturityInterest rate that makes the present value of the bond’s payments equal to its price.Solve the bond formula for rYield to Maturity Example10 yr Maturity Coupon Rate = 7%Price = \$950Solve for r = semiannual rater = 3.8635%Yield MeasuresBond Equivalent Yield 7.72% = 3.86% x 2Effective Annual Yield (1.0386)2 - 1 = 7.88%Current Yield Annual Interest / Market Price \$70 / \$950 = 7.37 %Realized Yield versus YTMReinvestment AssumptionsHolding Period ReturnChanges in rates affects returnsReinvestment of coupon paymentsChange in price of the bondHolding-Period Return: Single PeriodHPR = [ I + ( P0 - P1 )] / P0whereI = interest paymentP1 = price in one periodP0 = purchase priceHolding-Period ExampleCR = 8% YTM = 8% N=10 yearsSemiannual Compounding P0 = \$1000In six months the rate falls to 7% P1 = \$1068.55HPR = [40 + ( 1068.55 - 1000)] / 1000 HPR = 10.85% (semiannual)Holding-Period Return: MultiperiodRequires actual calculation of reinvestment incomeSolve for the Internal Rate of Return using the following:Future Value: sales price + future value of couponsInvestment: purchase priceRating companiesMoody’s Investor ServiceStandard & Poor’sDuff and PhelpsFitchRating CategoriesInvestment gradeSpeculative gradeDefault Risk and RatingsCoverage ratiosLeverage ratiosLiquidity ratiosProfitability ratiosCash flow to debtFactors Used by Rating CompaniesSinking fundsSubordination of future debtDividend restrictionsCollateralProtection Against DefaultDefault Risk and YieldRisk structure of interest ratesDefault premiumsYields compared to ratingsYield spreads over business cycles